Re: [中學] 100板橋高中教師甄選試題
※ 引述《RainIced (我好想念快速的宿網)》之銘言：
: 2.n > 4、n為正整數，S = {5、6、7、.....、n}，將S分成
: 兩個部份，至少有一個部份內有a、b、c，使得ab=c，其中
: a、b、c不需相異。求n 的最小值。
The answer is n=3125
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when n=3125
S1∪S2=S, S1∩S2= { }
We just point out the elements 5,25,125,625,3125.
The other elements are neglected.
(i) S1={5}, S2={25,125,625}, done
(ii) S1={5,25}, done
(iii) S1={5,125}, S2={25,625},done
(iv) S1={5,125,625}, done
(v) S1={5,625,3125}, done
(vi) S1={5,625}, S={25,125,3125}, done
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when n=3124
S1={5,6,...,24}
S2={25,26,...,624}
S3={625,626,...,3124}
if a,b in S1, then ab NOT in S1∪S3
if a,b in S2, then ab NOT in S2
if a,b in S3, then ab NOT in S1∪S3
if a in S1, b in S3,then ab NOT in S1∪S3
Then we can divides S into two parts S1∪S3 and S2.
Neither S1∪S3 nor S2 satisfy the required property.
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◆ From: 112.104.171.228
※ 編輯: JohnMash 來自: 112.104.171.228 (06/04 00:55)
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